Generalized Pascal functional matrix and its applications

Generalized Pascal k-eliminated functional matrix with 2n variables

The Generalized Pascal Matrix via the Generalized Fibonacci Matrix and the Generalized Pell Matrix

In [4], the authors studied the Pascal matrix and the Stirling matrices of the first kind and the second kind via the Fibonacci matrix. In this paper, we consider generalizations of Pascal matrix, Fibonacci matrix and Pell matrix. And, by using Riordan method, we have factorizations of them. We, also, consider some combinatorial identities.

-Riordan array for q -Pascal matrix and its inverse matrix

In this paper, we prove the q -analogue of the fundamental theorem of Riordan arrays. In particular, by defining two new binary operations ∗q and ∗1/q , we obtain a q -analogue of the Riordan representation of the q -Pascal matrix. In addition, by aid of the q -Lagrange expansion formula we get q -Riordan representation for its inverse matrix.

Generalized Inverse of a Matrix and Its Applications

The concept of an inverse of a singular matrix seems to have been first introduced by Moore [1], [2] in 1920. Extensions of these ideas to general operators have been made by Tseng [3], [4], [5], but no systematic study of the subject was made until 1955 when Penrose [6], [7], unaware of the earlier work, redefined the Moore inverse in a slightly different way. About the same time one of the au...

Coupled fixed points of generalized Kanann contraction and its applications

The purpose of this paper is to find of the theoretical results of fixed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized Kanann type contractivity of assumption. Also, as an application, we prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic bou...